Williams.] BIONIC VALUE OF FOSSILS. 125 
convey some idea of the important elements of form, it is actually 
necessary that either the original specimen or drawings illustrating 
the form be used to convey to the mind the meaning of the terms of 
the description. 
It becomes important, therefore, for stating scientifically the histor- 
ical relations of organisms, to find some method of measuring the dif- 
ference between one fossil and another which shall have mathematical 
value and be capable of expression in mathematical terms. 
In the crystal the relations of the faces to each other may be 
expressed in degrees and minutes of angle borne by the planes to 
each other, and their extent may be measured in millimeters. The 
chemical elements of which they are composed may be expressed in 
percentages of the total quantity of matter in the individual crystal, 
and these elements may be compared by their atomic weights or be 
expressed in terms of specific gravity. It is the form of a fossil which 
expresses the qualities of the organisms, but this form can not be 
expressed mathematically, nor is it coordinate with composition. 
Degree of complexity of organization is of prime importance in meas- 
uring the rank of the organisms in systematic classification. This 
degree of complexity, or amount of differentiation of structure, which 
is the basis of systematic classification, is evidence of the amount of 
evolution through which the ancestors of an individual have passed. 
For instance, the complex structure of the crayfish presents the 
morphological evidence of its taxonomic rank. It holds a higher rank 
in classification than does the trilobite. While thus much is known 
and is distinguishable in terms of form and use of organs — or, to speak 
abstractly, in terms of morphological characters— it is very difficult to 
express in mathematical terms the degree of difference or the relative 
rank of the organisms. In seeking for some such terms the practice in 
physics and chemistry may be studied. Both physics and chemistry 
have reached some degree of mathematical precision in expressing 
values of their phenomena by the adoption of arbitrary units, such 
as pound and foot, of which there can be preserved visible standards 
for comparison. Another set of standards are measures of exertion 
of force which is not visible but is capable of record in terms of the 
visible standards, pound and foot, with the help of the measures of 
time, duration, and motion in space. Such standards are the dyne 
and the ohm. When it is sought to measure the relative values of 
organisms, although their bodies are composed of chemical elements, 
it is found that their values are more than atomic. Although 1 hey are 
mechanically constructed and act in accordance with physical laws of 
matter, their values can not be expressed in terms of physics. 
The idea that the survival of organisms in competitive struggle is 
determined by the measure of vital energy exhibited by the several 
competitors furnishes a suggestion as to the kind of measure by 
which the values of organisms may be compared. 
